This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A159290 #12 Mar 23 2023 06:51:03
%S A159290 3,5,13,25,53,105,213,425,853,1705,3413,6825,13653,27305,54613,109225,
%T A159290 218453,436905,873813,1747625,3495253,6990505,13981013,27962025,
%U A159290 55924053,111848105,223696213,447392425,894784853,1789569705,3579139413
%N A159290 A generalized Jacobsthal sequence.
%C A159290 Sequence generated by the floretion: X*Y with X = 0.5('i + 'j + 'k + 'ee') and Y = 0.5(i' + j' + k' + 'ij' + 'ik' + 'ji' + 'jk' + 'ki' + 'kj' + 'ee')
%H A159290 G. C. Greubel, <a href="/A159290/b159290.txt">Table of n, a(n) for n = 0..1000</a>
%H A159290 Creighton Dement, <a href="http://fumba.eu/sitelayout/Floretion.html">Online Floretion Multiplier</a> [broken link]
%H A159290 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-2).
%F A159290 a(n) = -1 + (2*(-1)^n + 5*2^(n+1))/3.
%F A159290 G.f.: (3-x)/((1-x)*(1+x)*(1-2*x)).
%F A159290 a(n) = 3*A000975(n+1) - A000975(n). - _R. J. Mathar_, Sep 11 2019
%F A159290 a(n)+a(n+1) = A051633(n+1). - _R. J. Mathar_, Mar 23 2023
%t A159290 LinearRecurrence[{2, 1, -2}, {3, 5, 13}, 50] (* or *) Table[-1 + (2*(-1)^n + 5*2^(n+1))/3, {n,0,30}] (* _G. C. Greubel_, Jun 27 2018 *)
%o A159290 (PARI) x='x+O('x^50); Vec((3-x)/(-x^2+1-2*x+2*x^3)) \\ _G. C. Greubel_, Jun 27 2018
%o A159290 (Magma) [-1 + (2*(-1)^n + 5*2^(n+1))/3: n in [0..50]]; // _G. C. Greubel_, Jun 27 2018
%Y A159290 A083943, A068156
%K A159290 easy,nonn
%O A159290 0,1
%A A159290 _Creighton Dement_, Apr 08 2009